100 closed doors are each toggled by a passerby a number of times equal to their factors. Which doors end up open?
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There are 100 closed doors. The first person toggles every door, the second toggles every second door, the third every third door, and so on up to the hundredth person. Which doors are left open at the end?
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There are 100 closed doors. The first person toggles every door, the second toggles every second door, the third every third door, and so on up to the hundredth person. Which doors are left open at the end?
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Only the doors at perfect square numbers (1, 4, 9, 16, 25, 36, 49, 64, 81, 100) remain open, because only perfect squares have an odd number of factors.
